First of all, note that the term \(\frac{a}{t^p}x(t)\)  is a Tikhonov regularization term, which may assure the strong convergence of a generated trajectory to the minimizer of minimal norm of the objective function \(g.\) 
For further insight into the Tikhonov regularization techniques we refer to [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
